Disease concordance and sex similarity in twins.

Disease patterns in twins may show the presence of genetic or of environmental causes. Two arguments of inference have been used. Discordances between monozygotic twins have been taken to indicate the presence of environmental determinants; and high levels of concordance in monozygotic (MZ) pairs compared with dizygotic (DZ) pairs have been taken to indicate the presence of genetic causes. Neither argument is rigorous and, at this level, neither is quantitative. An investigator cannot always establish the zygosity of individual twin pairs, and many have therefore used indirect arguments, based upon Weinberg's differential method. Thus, the number of MZ pairs in a randomly selected sample of twin pairs may be estimated by subtracting the number of unlike-sexed (U) from the number of like-sexed pairs (L). The proportion of MZ pairs is then (L - U)/(L + U), and of DZ pairs 2U/(L + U). Cannings showed that in twins which are randomly selected, and when the proportion of males is 0·5, these formulae are maximum-likelihood estimators; also that their validity is unaffected by differential prenatal viability of MZ and DZ twins. However, in the context of investigating aetiologies we need to ask whether these relationships remain true in twins which are not selected randomly, but because a particular disease occurred in one or both of the pair. This distinction has not always been clearly made in the past. It turns out to be crucial. Smith, for example, was led to an erroneous conclusion with respect to the aetiology of Down's disease. This he later recognised, and showed that the formulation of a correct method for estimating the proportions of the MZ and DZ twins depended upon the prior choice of a model of pathogenesis. It was necessary to decide in advance whether the disease-determining events occurred before or after the point of MZ cleavage. Distortions of the Weinberg rule also occur in sex-linked recessive transmission where the U:L ratio among DZ pairs is other than 1:1; it is this ratio upon which the validity of the Weinberg method chiefly depends. For the investigator examining diseases the causes of which are not known, the necessity to make assumptions about the aetiology of the disease before he even begins his analysis introduces a disturbing circularity. These considerations provide the background to this paper.